/// <summary>
/// Delaunay triangulate point cloud with given convex hull.
/// Returns null if less than 3 points provided.
/// Using Tenamura-Merriam algorithm which does 'advancing front' starting with convexHull edges.
/// UNOPTIMAL IMPLEMENTATION! This will not deal with regular grids.
/// </summary>
/// <param name="points">Point cloud, list of Vector2 elements.</param>
/// <param name="points">Edge list, convex hull for point cloud.</param>
/// <returns>List of Edges defining the convex hull. Edges are not sorted but will have normals pointing away from the convex hull.</returns>
public static List <Triangle> Triangulate(List <Vector2> points, List <Edge> convexHull)
{
if (points.Count < 3)
{
// Not enough points to create triangulation -> return null
return(null);
}
#region Debug_Region_1
Vector3 LINE_ZOFFS = new Vector3(0, 0, 0.002);
int triCount = 0;
ReViewFeedManager debug = ReViewFeedManager.Instance;
long mesh_id = debug.AddMesh(debug.DebugTimer, -1, new Matrix4x4(), new Vector3(0, 0, 0.001), true);
#endregion
// Final list of convex hull edges
List <Triangle> triangles = new List <Triangle>();
List <Edge> edgesToProcess = new List <Edge>();
foreach (Edge edge in convexHull)
{
edgesToProcess.Add(edge.GetFlipped());
}
while (edgesToProcess.Count > 0)
{
Edge edgeToProcess = edgesToProcess[0];
edgesToProcess.RemoveAt(0);
int circumCircleFailCount = 0;
bool triangleAdded = false;
// Try to find third vertex for the edgeToProcess to form a triangle
List <int> testedCandidates = new List <int>();
for (int i = 0; i < points.Count; i++)
{
if (edgeToProcess.Contains(i))
{
// This point is part of the edge already -> Skip
continue;
}
if (!edgeToProcess.PointInFront(points, points[i]))
{
// This point is not in front -> Skip
continue;
}
if (testedCandidates.Contains(i))
{
// Already processed -> Skip
continue;
}
testedCandidates.Add(i);
Triangle t = new Triangle(edgeToProcess.A, edgeToProcess.B, i);
if (GeometryMath.IsTriangleDegenerate(points[t.A], points[t.B], points[t.C]))
{
// Degenerate triangle (no surface area so points are all in a line) -> Ignore this and continue
continue;
}
// Check circumcircle validity for this triangle
bool pointsInCircumCircle = false;
for (int j = 0; j < points.Count; j++)
{
if (i == j || edgeToProcess.Contains(j))
{
continue;
}
Vector2 otherPoint = points[j];
// Some other point -> Check if in circumcircle
if (t.PointInCircumcircle(points, otherPoint))
{
#region Debug_Region_2
// Add debug drawing for failed circumcircle tests
Vector2 center;
double radius;
if (GeometryMath.GetCircumcircle(points[edgeToProcess.A], points[edgeToProcess.B], points[i], out center, out radius))
{
Color32 debugColor = Color32.FromHSVA((double)circumCircleFailCount / 16.0 % 1.0, 0.9, 1.0, 1.0);
// Circumcircle
debug.AddCircle(debug.DebugTimer, debug.DebugTimerStep, (Vector3)center + LINE_ZOFFS, radius, new Vector3(0, 0, 1), 64, debugColor);
// Point that was inside (fails the test)
debug.AddBox(debug.DebugTimer, debug.DebugTimerStep, new Matrix4x4(new Quaternion(new Vector3(0, 0, 1), Math.PI * 0.25)), new Vector3(points[j].x, points[j].y, 0.0), new Vector3(0.015, 0.015, 0.015), debugColor);
// Lines to show triangle tested
debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, (Vector3)points[edgeToProcess.A] + LINE_ZOFFS, (Vector3)points[edgeToProcess.B] + LINE_ZOFFS, new Color32(0, 0, 0, 255));
debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, (Vector3)points[edgeToProcess.B] + LINE_ZOFFS, (Vector3)points[i] + LINE_ZOFFS, debugColor);
debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, (Vector3)points[i] + LINE_ZOFFS, (Vector3)points[edgeToProcess.A] + LINE_ZOFFS, debugColor);
debug.AdvanceDebugTimer();
}
#endregion
circumCircleFailCount++;
if (!testedCandidates.Contains(j))
{
i = j - 1;
}
pointsInCircumCircle = true;
break;
}
}
if (pointsInCircumCircle)
{
// Points in circumcircle -> Skip
continue;
}
// Update edgesToProcess list by adding two new edges if they are not one of the convex hull edges
Edge newEdgeA = new Edge(edgeToProcess.A, i);
Edge newEdgeB = new Edge(i, edgeToProcess.B);
// Check if new edges would be the same as unprocessed convex-hull edges
for (int j = 0; j < edgesToProcess.Count; j++)
{
Edge convexEdge = edgesToProcess[j];
if (convexEdge == newEdgeA)
{
// Don't add newEdgeA and remove convexEdge
newEdgeA = null;
edgesToProcess.RemoveAt(j);
j--;
}
else if (convexEdge == newEdgeB)
{
// Don't add newEdgeA and remove convexEdge
newEdgeB = null;
edgesToProcess.RemoveAt(j);
j--;
}
}
// Check if new edges would be shared with existing triangle edges
for (int j = 0; j < triangles.Count; j++)
{
if (triangles[j].Contains(newEdgeA))
{
newEdgeA = null;
}
if (triangles[j].Contains(newEdgeB))
{
newEdgeB = null;
}
if (newEdgeA == null && newEdgeB == null)
{
break;
}
}
if (newEdgeA != null)
{
edgesToProcess.Add(newEdgeA);
}
if (newEdgeB != null)
{
edgesToProcess.Add(newEdgeB);
}
// Valid triangle -> Add to delaunay set
triangles.Add(t);
#region Debug_Region_3
// Debug graphics for triangle to be added
Vector2 triCenter;
double triRadius;
// Add circumcircle
GeometryMath.GetCircumcircle(points[t.A], points[t.B], points[t.C], out triCenter, out triRadius);
debug.AddCircle(debug.DebugTimer, debug.DebugTimerStep, (Vector3)triCenter + LINE_ZOFFS, triRadius, new Vector3(0, 0, 1), 64, new Color32(255, 255, 0, 255));
// Add triangle lines
debug.AddLine(debug.DebugTimer, -1, (Vector3)points[t.A] + LINE_ZOFFS, (Vector3)points[t.B] + LINE_ZOFFS, new Color32(0, 0, 0, 255));
debug.AddLine(debug.DebugTimer, -1, (Vector3)points[t.B] + LINE_ZOFFS, (Vector3)points[t.C] + LINE_ZOFFS, new Color32(0, 0, 0, 255));
debug.AddLine(debug.DebugTimer, -1, (Vector3)points[t.C] + LINE_ZOFFS, (Vector3)points[t.A] + LINE_ZOFFS, new Color32(0, 0, 0, 255));
// Add triangle
debug.AddTriangle(mesh_id, debug.DebugTimer, points[t.A], points[t.B], points[t.C], new Color32(32, 255, 32, 128));
// Progress for console window
triCount++;
if (triCount % 100 == 0)
{
Console.WriteLine("TriCount {0}", triCount);
}
debug.AdvanceDebugTimer();
#endregion
triangleAdded = true;
// Processed 'edgeToProcess' -> Proceed to next in the list
break;
}
#region Debug_Region_4
// Debug graphics for the case when no triangle could be added for given edge
if (!triangleAdded)
{
long line_id = debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, (Vector3)points[edgeToProcess.A] + LINE_ZOFFS * 2, (Vector3)points[edgeToProcess.B] + LINE_ZOFFS * 2, new Color32(255, 0, 0, 255));
debug.AddAnnotation(line_id, debug.DebugTimer, debug.DebugTimerStep, "No valid triangle could be generated!", new Color32(255, 255, 255, 255));
debug.AdvanceDebugTimer();
}
#endregion
}
Console.WriteLine("Done triangles");
return(triangles);
}
